1. Field of the Invention
The present invention relates to a recording apparatus for recording an intermediate tone image.
2. Related Background Art
For reproducing an intermediate tone image in a pseudo manner with a recording apparatus poor in intermediate tone reproducing capability, there is already proposed and practiced the so-called dither method, the density pattern method, etc. These methods will not be explained in detail as they are the subject of various patent applications such as the Japanese Patent Laid-open 79677/1982 and are detailedly explained in detail in various references. These methods try to increase the number of density levels within a limited matrix size.
In the conventionally employed method, an intermediate tone image signal (image density signal) is compared with a threshold value signal (dither signal) for conversion into a binary signal or a multi-value signal of limited levels, and the intermediate tone is reproduced in a pseudo manner by the size or density of various dot.
In the case of using a threshold signal in the form of a 4.times.4 matrix, a recording apparatus capable of only reproducing two density levels can only reproduce 17 density levels. Consequently the density difference between the neighboring levels is large, so that the obtained image will have distinct pseudo contours. On the other hand, if the matrix is made larger for avoiding such a drawback, there will be a loss in the resolving power.
On the other hand, in a recording apparatus capable of recording plural density levels, it has been tried to increase the number of density levels by the use of plural density levels while maintaining a constant matrix size. For example, in an ink jet printer, the multiple density levels can be achieved by the size of the dots or the density of ink, and, in an electrophotographic laser beam printer, the multiple density levels can be attained by dividing the matrix in the main scanning direction and conducting pulse width modulation, as disclosed in the Japanese Patent Laid-open 99864/1982.
However, it has been difficult to render the density difference per level too small to be perceived because, in case of the ink jet printer, the number or dot sizes or ink densities is inevitably limited, or, in case of the electrophotographic laser beam printer, the pulse frequency inevitably has a practical limit.
In the following there will be explained the conventional art of the electrophotographic laser beam printer.
FIG. 1 is a block diagram of a conventional electrophotographic laser beam printer, employing the dither method or density method for achieving multiple density levels. Its structure and the function will now be explained.
An image memory 21, for storing intermediate tone image data of 6 bits per pixel, receives addressing pixel data N1, designated by an address counter 22 for counting clock pulses CP and a main scanning synchronization signal (horizontal synchronization signal) BD to be explained later. A look-up table 23 converts the tone characteristic of the pixel data N1 into linearly corrected pixel data N2 and supplies the same to a digital comparator 24. The look-up table 23 effects a (N1-N2) conversion by adapting the pixel data N1 to a different address. The digital comparator 24 also receives an output T from a memory 31, storing a threshold value matrix, and compares the two input signals to release a binary signal V, which is used for driving a semiconductor laser 26 through an amplifier 25. A light beam emitted by the semiconductor laser 26 is reflected by a rotary polygonal mirror 27, rotated as indicated by an arrow, and effects main scanning on a photosensitive drum 28. The drum 28 is rotated in a direction as indicated by an arrow for sub scanning, and two-dimensional scanning is achieved in this manner. A latent image is formed on the drum 28 through an unshown electrophotographic process combined with the scanning with the beam I, and image recording is effected by image development with toner, image transfer and image fixing. A part of the beam I is reflected by a mirror 29, and enters a photodetector 30 to obtain the main scanning synchronization signal BD.
The memory 31 is composed of a matrix of 16.times.4, of which the column address in the main scanning direction is designated by a 16-bit column address counter 32 for counting the clock pulses CP, while the row address in the sub-scanning direction is designated by a 4-bit row address counter 33 for counting the main scanning synchronization signal BD. Consequently a pixel stored in the image memory 21 is converted into a density pattern corresponding to the entire memory 31, if the address counter 22 designates a pixel succession in the main scanning direction at every 16 counts of the clock pulses CP and in the sub-scanning direction at every 4 counts of the synchronization signals BD. On the other hand, if the address counter 22 renews the address at every 8 counts of the clock pulses CP and at every 2 counts of the synchronization signal BD, each pixel corresponds to 1/4 of the memory 31 to achieve an intermediate state between the dither method and the density pattern method. Such state is disclosed in detail in the Japanese Patent Laid-open 99867/1982.
In the present example in which each pixel contains data of 6 bits, the image data N1, N2 and the output T respectively assume a value from 0 to 63, and, when the level of the pixel data N2 is higher than that of the output T, the binary signal V assumes a level "1" to activate the semiconductor laser 26. However, the density characteristic of the obtained image depends on the arrangement of the threshold values in the memory 31, the emission intensity of the semiconductor laser 26, the electrophotographic process employed, etc.
FIG. 2 is a chart showing the relationship between the pixel data N1, N2 and the output image density D, wherein a curve (a) indicates the density D obtained from the pixel data N1 without using the look-up table 23, while a curve (b) indicates the density D obtained from the pixel data N2 after going through the look-up table 23. The ordinate represents the output image density, while the abscissa represents the pixel data. The output density for each pixel data changes stepwise for each pulse.
As will be seen in the curve (a), in the absence of slope correction, the change in the density is steeper in the low density range and slower in the high density range due to a large beam diameter. The maximum density difference per level .DELTA.D.sub.max appears between the level 5 and 6 of the pixel data N1. In actual measurement, .DELTA.D.sub.max =D.sub.2 -D.sub.1 =0.08. The human ability of perceiving a density difference is considered to be in a range of 0.01. Consequently a density difference of 0.08 is clearly perceivable. Thus the tonal characteristic of the output image is observed stepwise, with so-called pseudo contours. In this manner the tonal rendition is significantly deteriorated. Consequently the characteristic (a) cannot be considered acceptable in terms of tonal rendition. On the other hand, the curve (b) shows a case of correcting the tonal characteristic linearly. For example the levels 11-14 of the data N1 are converted to a level 5 in the data N2, and the levels 15-18 are converted to a level 6. This conversion expands a steep portion of the curve (a) and compresses a nonsteep portion. Consequently this conversion converts a pixel data to the data N.sub.2 or the curve (b).
However, such conversion does not change the maximum density difference per level .DELTA.D.sub.max, so that the tonal rendition is still unsatisfactory due to the presence of distinct pseudo-contours. This phenomenon becomes evident in a steep portion of the curve (a) or (b), thus deteriorating the tonal rendition in the portion.
Now reference is made to FIGS. 3A-3D and 4 for explaining the exposure distribution characteristic of a laser beam and the density distribution characteristic of an obtained image.
FIGS. 3A to 3D show waveforms for the explaining exposure distribution characteristic of the conventional pulse width modulation. FIG. 3A shows a laser driving pulse, and the laser beam is emitted when the pulse is at the state "1".
FIG. 3B shows the distribution of the intensity I of the laser beam along the ordinate, as a function of distance along the abscissa, and the distribution can be ordinarily approximated by a Gaussian distribution.
Thus, when normalized at the central intensity, the laser beam intensity I can be represented by: EQU I=exp(-x.sup.2 /2.sigma..sup.2) (1)
wherein x is the distance from the center, and .sigma. is the standard deviation in the Gaussian distribution.
The diameter of a laser beam is usually represented by a half-value width, i.e. a width where the intensity falls to 1/2 of the central intensity, or by a width where the intensity falls to 1/e.sup.2 of the central intensity. In the present text the latter method is adopted. Thus the diameter becomes equal to 4.sigma. shown in FIG. 3B. The laser beam scans at a speed v in a direction of the arrow at the lower right portion of FIG. 3B. Thus the scanning distance is represented by: EQU L=vT (2).
If the scanning speed is constant, L and T are equivalent so that FIGS. 3A and 3B can be viewed with a same scale.
FIG. 3C shows the intensity distributions, respectively in full line and broken line, at points Q and S, and FIG. 3D shows the distributions of exposure, by curves (a) and (b), respectively corresponding to exposure times T1 and T2.
The above-explained apparatus functions in the following manner.
It is assumed that the laser beam is turned on at P and off at Q, corresponding to a period T1 shown in FIG. 3A. Thus the intensity distribution immediately after the laser beam is turned on at P corresponds to FIG. 3B, while that immediately before the beam is turned off at Q corresponds to the full-lined curve in FIG. 3C. Consequently the beam intensity at P varies from the intensity I in FIG. 3B (center P) to the intensity in FIG. 3C (center Q), and the amount of exposure Ep at the point P is represented by: ##EQU1## wherein P-Q is the distance between the points P and Q.
Similarly the amount of exposure E.sub.Q at Q which is symmetrical to P in the Gaussian distribution is represented by: EQU E.sub.P =E.sub.Q ( 4).
Also the amount of exposure E.sub.R at a central point R between P and Q is given by: ##EQU2## In this manner the distribution of exposure when the laser beam is turned on for a period T1 is represented by the curve (a) in FIG. 3D.
Also if the laser beam shown in FIG. 3A is turned on for a double period T2 (=2T1), the intensity distribution immediately before it is turned off assumes a form represented by the broken-lined curve in FIG. 3C, and the amount of exposure at P becomes equal to the area hatched with horizontal lines in FIG. 3C. The exposure distribution in this case is represented by the curve (b) in FIG. 3D, and the center of the exposure distribution is shifted from R to Q.
FIG. 4 shows a density characteristic corresponding to the exposure distribution shown in FIG. 3D, wherein the first quadrant indicates the output density D along the scanning function in ordinate as a function of the distance L along the abscissa. The second quadrant shows the density along the ordinate as a function of the amount of exposure E in a recording system, for example an electrophotographic process. The electrophotographic process may be designed as an image scanning process, in which the density is higher for a larger exposure, or a background scanning process, in which the density is lower for a larger exposure, and the former is adopted in this case. The third quadrant shows the exposure distribution shown in FIG. 3D, wherein abscissa indicates the distance L.
The exposure distribution shown in the third quadrant provides a visible image of the density distribution shown in the first quadrant, relying on the E-D characteristic shown in the second quadrant. Curves (a) and (b) in the first quadrant correspond to those in FIG. 3D, respectively indicating the density distributions for the beam turn-on periods T1, T2. The average density is obtained by integrating a three-dimensional distribution obtained from the distribution in the first quadrant and from the distribution in the scanning direction, divided by unit area. However, the two-dimensional distribution will not be considered since two-dimensional consideration in the scanning and orthogonal directions is quite complex while one-dimensional consideration in the scanning direction alone is sufficient for qualitative understanding. In such one-dimensional consideration, a value obtained by integrating the waveform shown in the first quadrant and dividing by the distance can be considered equivalent to the average density. The area ratio in the first quadrant is not equal to the ratio of the beam turn-on periods due to the non-linearity of the E-D characteristic, but it will be understood that the density becomes higher and the dot diameter becomes larger as the laser beam is turned on longer.
Also it will be understood that, due to the narrow latitude of the electrophotographic process, a beam turn-on period longer than T2 results in the density saturation and gives rise to an increase in the dot diameter as represented by a curve (c) in the first quadrant.
As explained in the foregoing, it has been tried to obtain multiple density levels, utilizing the narrow latitude of the electrophotographic process. However, in the formation of a black dot in a highlight area as shown by the curves (a) and (b) in the first quadrant in FIG. 4, there results a black dot having a small area but a nearly saturated density, as represented by the curve (b). Such a black dot, being smaller in area than the white area and having a high density, is quite conspicuous, thus giving a coarse impression in the high-light area of the image.
In certain apparatus such as the electrophotographic laser beam printer, the main scanning is effected by deflecting the laser beam with a rotary polygonal mirror, while the sub scanning is effected by the rotation of a photosensitive drum. The limitation in the working precision and mounting precision of the rotary polygonal mirror results in unevenness in the main scanning, while the limitation in the precision of rotation of the photosensitive drum results in fluctuation in the rotation, thus giving rise to fluctuation in density in the sub scanning direction.
In the following there will be explained a process by which a fluctuation in scanning results in a fluctuation in density, in an electrophotographic laser beam printer.
The average exposure E per unit length in the sub scanning direction is given by: EQU E=I.multidot.T.sub.H .multidot.N (6)
wherein I is the laser beam intensity, T.sub.H is the main scanning time, and N is the average number of scanning lines per unit length in the sub scanning direction. In the presence of a fluctuation in the main scanning or rotation, the number N of scanning lines fluctuates by .DELTA.N, and the variation .DELTA.E in exposure is given by: EQU .DELTA.E=I.multidot.T.sub.H .multidot..DELTA.N (7)
In actual image recording, the intensity I is modulated. However, if I is assumed to be constant in order to consider the fluctuation, there will result .DELTA.E.alpha..DELTA.N because the main scanning time T.sub.H is constant.
In the electrophotographic process, an exposure of the photosensitive drum results in a potential latent image, which is converted into an image density through the steps of development with toner, image transfer and image fixing, but the relationship between the amount of exposure and the image density is generally non-linear. Though the electrophotographic process is provided with a narrow latitude, the characteristic can be partly approximated by a linear line. For the simplicity of explanation, the density is approximated as proportional to N, so that .DELTA.D.alpha..DELTA.N.
Consequently there is obtained a relation: EQU .DELTA.D/D.alpha..DELTA.N/N (8)
The average or effective value .DELTA.N.sub.RMS of .DELTA.N is determined by the precision of the hardware and can be considered almost constant. Since N is constant, the ratio of .DELTA.N.sub.RMS and N is also constant and assumed as Cv. Thus the effective value .DELTA.D.sub.RMS of .DELTA.D has a relation: EQU .DELTA.D.sub.RMS .alpha.Cv.multidot.D (9)
thus the fluctuation in density is proportional to the average density. As the amount of exposure is not proportional to the density in practice, the relation (9) does not stand in a strict sense, but it will be understood that the fluctuation in density becomes larger for a higher average density. However, since the density becomes saturated in excess of a certain exposure, the density does not vary even if the amount of exposure varies. Therefore, in the case of reproducing the intermediate tone with binary levels of black and white, the fluctuation in density does not appear if the laser beam intensity is elevated to saturate the density. However the laser beam intensity distribution is not rectangular but is close to a Gaussian distribution, and the exposure distribution in the main scanning direction is given by the integration of the Gaussian curve passing through each point, having a prolonged sloping portion. Thus, if the laser beam is turned off only for a brief period, the exposure is not reduced to zero because of the overlapping slope portions, thus resulting in the aforementioned fluctuation in density.
FIGS. 5A-5E and 6A-6E illustrate the cause of the fluctuation in density. FIGS. 5A and 6A show laser driving pulses, wherein T1 and T2 are turn-on periods. FIGS. 5B and 6B show the Gaussian distributions of the laser beam intensity I, and FIGS. 5C and 6C show corresponding exposure distributions, FIGS. 5D and 6D show the distributions of electric field intensity corresponding to the exposure distributions shown in FIGS. 5C and 6C, and FIGS. 5E and 6E illustrate output density distributions corresponding to the electric fields shown in FIGS. 5D and 6D.
If the beam turn-on time T1 is short as shown in FIG. 5A, no overlapping appears in the exposure distribution as shown in FIG. 5C. As already known well, the electrophotographic process provides a so-called edge effect, by which the edges of the image are emphasized more strongly than in the potential distribution which is determined by the exposure distribution. The exposure distribution shown in FIG. 5C provides an electric field distribution in FIG. 5D, which gives rise to a density distribution shown in FIG. 5E. Thus the obtained dot is poorer in the intermediate tone than in the exposure distribution.
On the other hand, if the beam turn-on period is long as shown in FIG. 6A, the sloping portions mutually overlap as shown in FIG. 6C to provide an exposure distribution shown by a broken line. Thus the electric field intensity distribution is also lowered as shown in FIG. 6D to provide an intermediate density. Also at the center of a dot, the density is lowered by a reduced edge effect. The density at the center of the beam turn-off period is a fluctuated density .DELTA.D due to the aforementioned fluctuation in exposure .DELTA.E.
Thus, in the case of representing an intermediate tone in binary densities, the fluctuation in density scarcely appears in the image development if the black dot has a small area, or in a high-light area where the average density is low. However, in an area with a higher average density where the black dots have a larger area, there will result a fluctuation in the density. In this manner the fluctuation in density becomes larger as the average density increases already explained before. On the other hand, in the case of representing the intermediate tone with multiple density levels, the fluctuation in density is naturally present but can be reduced significantly if the multiple levels are used only in the high-light area. Also in the case of background development, the fluctuation in density may inversely appear in the high-light area.
FIG. 7 schematically shows the relationship between the intermediate tone image input signal N along the abscissa and the output image density D along the ordinate, wherein D.sub.p represents the density level of the recording material.
As will be apparent from FIG. 7, the output image density fluctuates more strongly in the high density area.
As explained in the foregoing, the conventional image recording apparatus has been associated with a drawback that it is incapable of stably recording an intermediate tone image in the low density area or in the high density area.